I read a book where they had a method of compressing matter into neutronium and keeping it that way, so they turned the interior of the moon into it until it was dense enough to hold air.

1) That's not something we can actually do in reality, at least not now or in the foreseeable future, 2) that would not change the mass of the Moon, so it would be useless. It would only destroy the Moon by changing its internal structure. But this is extremely off topic here.